Question

Use the recursively defined geometric sequence a1=56
, an=4an−1
and find the common ratio.

Answer 1

In a geometric sequence, the common ratio \( r \) is the factor by which we multiply each term to get the next term.

Given the recursively defined geometric sequence:

- The first term \( a_1 = 56 \)
- The recursive definition \( a_n = 4a_{n-1} \)

From the recursive relation, we can see that each term is obtained by multiplying the previous term by 4.

Thus, the common ratio \( r \) for this geometric sequence is:

\[
r = 4
\]

Therefore, the common ratio of the sequence is \( 4 \).